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In mathematics, the Kallman–Rota inequality, introduced by Kallman & Rota (1970), is a generalization of the Landau–Kolmogorov inequality to Banach spaces. It states that if A is the infinitesimal generator of a one-parameter contraction semigroup then

$${\displaystyle \|Af\|^{2}\leq 4\|f\|\|A^{2}f\|.}$$

References

Kallman, Robert R.; Rota, Gian-Carlo (1970), "On the inequality $$\Vert f^{{\prime }}\Vert ^{{2}}\leqq 4\Vert f\Vert \cdot \Vert f''\Vert$$ ", Inequalities, II (Proc. Second Sympos., U.S. Air Force Acad., Colo., 1967), New York: Academic Press, pp. 187–192, MR 0278059.